Function generator for producing the possible boolean functions of eta independent variables



July 29, 1969 w. H. HANSON 3, 58,240

FUNCTION GENERATOR FOR PRODUCING THE POSS]: BOOLEAN FUNCTIONS OF nINDEPENDENT VARIABL Filed Dec. 28. 1965 Y I 2 .I

l I l I I I I I I I I I I I I I INVENTOR WILLIAM H. HANSON Y c l j I 4 II BY I ATT RNEY United States Patent US. Cl. 328-92 3 Claims ABSTRACT OFTHE DISCLOSURE A switching network for producing any one of the possibleBoolean functions of n independent variables which comprise a pluralityof majority decision logic elements interconnected in such a manner thatin going from n independent variables to n+1 independent variables onlyone additional logic level of majority decision logic elements isnecessitated.

This invention relates to function generators and, more particularly,provides means for generating any one of the 2 possible Booleanfunctions of n independent variables.

It has been determined that; if the logical function,

(where denotes any logical expression), is representative of an n1variable function generator, such that for a given set of values x x ofthe n-l independent variables, X X,,

reduces to #X #Y (where Y is one of the 2 function selection signals ofthe function generator, and k=2 x +2 x +x then is representative of an nvariable function generator where,

f.= n#( )1# )m, fir equivalent to with function selections signals, Ycontained in being replaced by, Y where j=2k if k 2 j=2k+l if k 2 and n=n# 1# r )m. )1

being equivalent to with function selection signals, Y contained inbeing replaced by, Y,- where The effect of this determination is thattwo slightly modified n-1 variable function generators may be combinedwith a single three input majority logic element utilizing oneadditional logic level to provide an n variable function generator.Further, the resulting n variable function generator meets the criterionset forth above for f so that two slightly modified n variable functiongenerators designed in accordance with this invention may be combined toform an n+1 variable function generator.

There are a variety of logical functions meeting the criterion set forthabove which can be utilized in effecting this invention. For example,see m-Out-of-n Decision Logic by Raship appearing in Proceedings of TheNational Electronics Conference, vol. XIX, 1963.

The novel features which are considered characteristic of this inventionare set forth with particularity in the appended claims. The inventionitself both as to its organization and method of operation, as well asadditional advantages thereof, will be best understood from thefollowing example when read in connection with the accompanying drawing,in which:

FIGURE 1 is a logical block diagram of an n1 (n=3) variable functiongenerator of the type to be utilized in accordance with this invention;and

FIGURE 2 is an example of an 11 (11:3) variable function generatorconstructed in accordance with this invention utilizing two n1 functiongenerators of the type shown in FIGURE 1.

In the drawing each of the blocks represent a three input majority logicelement. Arrowheads indicate direction; each normal arrowhead representsa normal signal; each small circle arrowhead represents a negatedsignal.

.With reference now to FIGURE 1 of the drawing, a logical block diagramof a two variable function generator of the type to be utilized with theinstant invention is shown. The function generator, designated by thereference numeral 100, for generating a signal representative of, f(X Xcomprises a network of seven majority logic elements arranged in threelogic levels. Function generator receives signal representations ofindependent variables, X and X and function selection signals, Y Y Y andY and generates an output signal in accordance with the logicalfunction:

two variable function generator shown in FIGURE 1. The function, f(X Xis such that,

reduces to #X #Y for each member of the set of all possible values ofthe two independent variables, X and X (the set comprising (0, 0), (0,1), (1, 0), and (l, 1)). Y designates the value of the functioncorresponding to that number (x x of the above described set for which,k=2x +x For example, when X =X =0,

ent variables take on the values X =0 and X =l, X =l and X =0, and X =1and X =1,

reduces to respectively.

The values of the function selection signals, Y corre sponding to aparticular function are easily determined. Function selection signalscorresponding to assignments of values to the independent variables forwhich the function takes the value one are assigned the value one andthose corresponding to assignments of values to the independentvariables for which the function takes the value zero are assigned thevalue zero. For example, if,

(the exclusive-OR function) is the function to be generated, thenobviously Y =Y :0 and Y =Y =l.

With reference now to FIGURE 2 of the drawing, a logical block diagramof a three variable function generator designed in accordance with thisinvention is shown. The three variable function generator comprises twoslightly modified two variable function generators designated byreference numerals 100 and 100", arranged in parallel and coupled tomajority logic element 20. The three variable function generatorreceives signal representations of independent variables, X X and X andfunction selection signals Y Y Y Y Y Y Y and Y and generates an outputsignal in accordance with the logical function;

A signal representative of,

is generated by the network designated by reference numeral 100'.Network 100' is substantially identical with network 100 with theexception of an input signal representation received by the element fromwhich the output signal is derived (i.e.: element and function selectionsignals, Y The input signal representation of Y received by element 10of network 100 is replaced by a signal representation of i when receivedby element 10' of network 100'. Function selection signals, Y of network100 are transformed to function selection signals, Y,, of network 100 bythe following transformation:

Hence, Y Y Y Y Y Y and Y Y A signal representative of,

Element 20 receives signal representations of f,, f,,, and X andgenerates an output signal in accordance with the logical function:

The values of the function selection signals, Y corresponding to aparticular function are easily determined. Function selection signalscorresponding to assignment of values to the independent variables forwhich the function takes the value one are assigned the value one,

,.4 and those corresponding to assignments of values to the independentvariables for which the function takes. the value zero are assigned thevalue zero. For example, if (X -X )+X is the function to be generated,then Obviously Y1:Y3:Y5:Y6:Y7:1 and Y0:Y2:Y4:0.

The example shown in the drawing and described above (i.e.: with n=3) isto be construed as exemplary only and not limitative. It is understoodthat suitable modifications may be made in the structure as disclosedprovided such modifications come within the spirit and scope of theappended claims.

Having now, therefore, fully illustrated and described my invention,what I claim to be patentably novel and desire to protect by LettersPatent is:

1. A function generator, for generating a signal representative of iwhere f is any one of the 2 Boolean functions of n independent variablesX X X comprising:

input means for receiving signal representations of independentvariables X X X and 2 function selection signals, Y and means coupled tosaid input means for utilizing said independent variable signalrepresentations and said function selection signals to generate anoutput signal representative of f in accordance with the logicalfunction,

.fn 1#fa#fB 2. A function generator as defined in claim 1 in which saidgenerating means comprises:

a first network coupled to said input means for generating a signalrepresentative of f, in accordance with the logical function and asecond network coupled to said input means for generating a signalrepresentative of f, in accordance with the logical function 3. Afunction generator as defined in claim 2 in which said generating meansfurther comprises a three input majority logic element coupled to saidinput means, said first network, and said second network for utilizingsignal representations of 2 f,, and f to generate an output signalrepresentative of i References Cited UNITED STATES PATENTS 3,201,7018/1965 Maitra 307204 X OTHER REFERENCES Smith et al.: I.B.M. TechnicalDisclosure Bulletin, vol. 6, No. 4, September 1963, pp. 67-68.

DONALD D. FORRER, Primary Examiner US. Cl. X.R.

